Construction of equivalence maps in pseudo-Hermitian geometry via linear partial differential equations

• Ozawa Tetsuya

  Department of Mathematics Meijo University

• Sato Hajime

  Graduate School of Mathematics Nagoya University

抄録

We discuss an equivalence problem of pseudo-Hermitian structures on 3-dimensional manifolds, and develop a method of constructing equivalence maps by using systems of linear partial differential equations. It is proved that a pseudo-Hermitian structure is transformed to a standard model of pseudo-Hermitian structure constructed on the Heisenberg group if and only if it has the vanishing pseudo-Hermitian torsion and the pseudo-Hermitian curvature. A system of linear partial differential equations whose coefficients are associated with a given pseudo-Hermitian structure is introduced, and plays a central role in this paper. The system is integrable if and only if the pseudo-Hermitian structure has vanishing torsion and curvature. The equivalence map is constructed by using a normal basis of the solution space of the system.

収録刊行物

• ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ

  ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ 34 (1), 105-123, 2011

  国立大学法人 東京工業大学理学院数学系

キーワード

• General Mathematics

詳細情報

• CRID: 1390001205272370816
• NII論文ID: 130004496128
• DOI: 10.2996/kmj/1301576765
• ISSN: 18815472
• ISSN: 03865991
• MRID: 2786784
• 本文言語コード: en
• データソース種別:
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• 抄録ライセンスフラグ: 使用不可